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AP EAMCET202022 Sep 2020Morning ShiftMathematicsCircleActual

The area of the quadrilateral formed by the tangents from the point (4,5) to the circle x^2+y^2-4 x-2 y-11=0 , with a pair of radii joining the points of contact of these tangents is

Options

  1. A4
  2. B6
  3. C8
  4. D10

Correct answer

C. 8

Step-by-step solution

Equation of given circle aligned & & x^2+y^2-4 x-2 y-11 & =0 & & (x-2)^2+(y-1)^2 & =16 aligned From the figure, the area of quadrilateral P A C B aligned & =2 Area of P A C & =2 1 2 4 (A P) aligned and aligned A P & = length of tangent & = 16+25-16-10-11 =2 aligned Therefore area of the required quadrilateral =8 sq . units

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